Hom-quantum groups II: cobraided Hom-bialgebras and Hom-quantum geometry

2009/07/10 by Donald Yau, Yau, Donald · 4 citations
Mathematics · #16W30 #17A30 #17B37 #17B62 #81R50 #Advanced Operator Algebra Research #Advanced Topics in Algebra #Algebraic structures and combinatorial models #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Quantum Algebra (math.QA) #Rings and Algebras (math.RA)

paper · pdf · doi:10.48550/arxiv.0907.1880

openalex publication_date 2009/07/10 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

A class of non-associative and non-coassociative generalizations of cobraided bialgebras, called cobraided Hom-bialgebras, is introduced. The non-(co)associativity in a cobraided Hom-bialgebra is controlled by a twisting map. Several methods for constructing cobraided Hom-bialgebras are given. In particular, Hom-type generalizations of FRT quantum groups, including quantum matrices and related quantum groups, are obtained. Each cobraided Hom-bialgebra comes with solutions of the operator quantum Hom-Yang-Baxter equations, which are twisted analogues of the operator form of the quantum Yang-Baxter equation. Solutions of the Hom-Yang-Baxter equation can be obtained from comodules of suitable cobraided Hom-bialgebras. Hom-type generalizations of the usual quantum matrices coactions on the quantum planes give rise to non-associative and non-coassociative analogues of quantum geometry.

Cited by

• BiHom-Lie brackets and the Toda equation
• Hom-bialgebras and comodule Hom-algebras
• Paradigm of Nonassociative Hom-algebras and Hom-superalgebras
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